Factorizations of monoids are studied. Two necessary and sufficient conditions in terms of the so-called descent 1-cocycles for a monoid to be factorized through two submonoids are found. A full classification of those factorizations of a monoid whose one factor is a subgroup of the monoid is obtained. The relationship between monoid factorizations and non-Abelian cohomology of monoids is analyzed. Some applications of semi-direct product of monoids are given.
|Journal||Journal of Algebra and its Applications|
|Publication status||Accepted/In press - 2023|
- descent cohomology
- monoid action
ASJC Scopus subject areas
- Algebra and Number Theory
- Applied Mathematics